I am porting my application on Google App Engine with my personal gmail account. As part of application I have to send email to my application users regarding their content. I am able to send mails using my personal account(i.e myma...@gmail.com). But that's not good. I want to send mails from sup...@mydomai.com/info@mydomain.com to represent my company. For that I bought a domain from godaddy.com and registered with third party mail provider zoho.com.
From the link on the "learn more" in your error message, we specifically state that you need to have a gmail or Google domain, so you won't be able to use mydomai.com to do this. YOu will need to either use the appspotmail, or a gmail.
To use the email you want, I would suggest using something like SendGrid, which will provide more flexibility in that regards.